Examples
Polynomial equations appear in a wide variety of topics.
Applications in the Sciences
Polynomial systems arising from Nash equilibria
A story about how game theory meets multilinear systems and product of simplices.
Alt's problem
A classical problem from robotics
Computer vision
Triangulation of a dinosaur
Bacillus Subtilis
environmental and energy stress response of the bacterium Bacillus subtilis
Cyclooctane
The conformation space of cyclooctane
Rolling shutter cameras
Absolute pose estimation for a rolling shutter camera
The 6R-serial link robot
Using HomotopyContinuation.jl for a problem in kinematics
Energy minimization
Computing a macroscopic configuration
Mathematics of Data
Low rank tensor recovery
Reconstructing a tensor from linear measurements
The reach of a plane curve
Computing the reach
Sampling and Homology via Bottlenecks
Sampling an algebraic variety and computing its homology
Computing a logarithmic Voronoi cell
An adventure at the intersection of statistics and nonlinear algebra.
Sampling a probability distribution on a variety
By intersecting with linear spaces
Method of moments
For mixtures of three Gaussians
The point on a variety that minimizes the distance to a given point
Computing critical points
Monte Carlo integration
Integrating functions on a variety
Algebraic Geometry
When do two ellipses meet?
Let two ellipses grow until they intersect
Symmetroids
Computing the degree of a cubic symmetroid
Tensor decomposition and homotopy continuation
Using homotopy continuation for computing the CPD of a tensor
Tritangents
Using HomotopyContinuation.jl for computing tritangents of sextic curves
Curvature of plane curves
How to compute curvature
3264 conics tangent to five conics
All of them can be real.
The number of circles that are tangent to 3 given conics
Using HomotopyContinuation.jl for a problem in enumerative geometry